mass fractions of 4-methylbenzylmagnesium chloride

4-methylbenzylmagnesium chloride | elemental composition

Find the elemental composition for 4-methylbenzylmagnesium chloride in terms of the atom and mass percents: atom percent = N_i/N_atoms × 100% mass percent = (N_im_i)/m × 100% Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i, m_i, N_atoms and m using these items. • Finally, compute the percents and check the results. Write the chemical formula: C_6H_4CH_3CH_2MgCl Use the chemical formula to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms, per molecule: | number of atoms C (carbon) | 8 Cl (chlorine) | 1 H (hydrogen) | 9 Mg (magnesium) | 1 N_atoms = 8 + 1 + 9 + 1 = 19 Divide each N_i by N_atoms to calculate atom fractions. Then use the property that atom fractions must sum to one to check the work: | number of atoms | atom fraction C (carbon) | 8 | 8/19 Cl (chlorine) | 1 | 1/19 H (hydrogen) | 9 | 9/19 Mg (magnesium) | 1 | 1/19 Check: 8/19 + 1/19 + 9/19 + 1/19 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 8 | 8/19 × 100% = 42.1% Cl (chlorine) | 1 | 1/19 × 100% = 5.26% H (hydrogen) | 9 | 9/19 × 100% = 47.4% Mg (magnesium) | 1 | 1/19 × 100% = 5.26% Look up the atomic mass, m_i, in unified atomic mass units, u, for each element in the periodic table: | number of atoms | atom percent | atomic mass/u C (carbon) | 8 | 42.1% | 12.011 Cl (chlorine) | 1 | 5.26% | 35.45 H (hydrogen) | 9 | 47.4% | 1.008 Mg (magnesium) | 1 | 5.26% | 24.305 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molecular mass, m: | number of atoms | atom percent | atomic mass/u | mass/u C (carbon) | 8 | 42.1% | 12.011 | 8 × 12.011 = 96.088 Cl (chlorine) | 1 | 5.26% | 35.45 | 1 × 35.45 = 35.45 H (hydrogen) | 9 | 47.4% | 1.008 | 9 × 1.008 = 9.072 Mg (magnesium) | 1 | 5.26% | 24.305 | 1 × 24.305 = 24.305 m = 96.088 u + 35.45 u + 9.072 u + 24.305 u = 164.915 u Divide the mass for each element by m to calculate mass fractions. Then use the property that mass fractions must sum to one to check the work: | number of atoms | atom percent | mass fraction C (carbon) | 8 | 42.1% | 96.088/164.915 Cl (chlorine) | 1 | 5.26% | 35.45/164.915 H (hydrogen) | 9 | 47.4% | 9.072/164.915 Mg (magnesium) | 1 | 5.26% | 24.305/164.915 Check: 96.088/164.915 + 35.45/164.915 + 9.072/164.915 + 24.305/164.915 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 8 | 42.1% | 96.088/164.915 × 100% = 58.27% Cl (chlorine) | 1 | 5.26% | 35.45/164.915 × 100% = 21.50% H (hydrogen) | 9 | 47.4% | 9.072/164.915 × 100% = 5.501% Mg (magnesium) | 1 | 5.26% | 24.305/164.915 × 100% = 14.74%

Mass fraction pie chart